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Concept module

Total Internal Reflection

Push a ray from a higher-index medium toward a lower-index boundary, watch the critical angle emerge, and see the same live diagram hand off from ordinary refraction to full internal reflection.

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Why it behaves this way

Explanation

Total internal reflection is not a separate boundary law sitting beside refraction. It is the point where Snell's law stops giving a real transmitted angle because the light is trying to leave a higher-index medium for a lower-index one too steeply.

This concept keeps one compact boundary in charge. The incident angle, refractive-index contrast, critical-angle readout, reflected path, graph previews, prediction mode, compare mode, quick test, and worked examples all stay tied to the same live boundary state so the handoff from ordinary refraction to full internal reflection stays honest.

Key ideas

01Total internal reflection only becomes possible when light starts in the higher-index medium and tries to enter a lower-index medium, so n_1 must be larger than n_2 in the chosen travel direction.
02The critical angle satisfies sin(theta_c) = n_2 / n_1, so a larger index contrast lowers theta_c and makes internal reflection happen at smaller incident angles.
03As theta_1 approaches theta_c from below, the transmitted ray opens until it skims along the boundary at theta_2 = 90 degrees. Above that limit there is no real transmitted angle.
04Once the ray keeps reflecting inside the higher-index region, you have the same local event that fiber-optic guidance relies on, even though this page stays focused on one boundary.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough
Work from the boundary you are already editing. The substitutions pull from the live indices and incident angle, and the same state stays visible on the ray diagram and threshold graphs.

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Frozen valuesUsing frozen parameters

For the current media pair, what critical angle does this boundary allow?

Incident-medium index

1.52

Transmitted-medium index

1

Critical angle

41.14 °

1. Check the travel direction

A critical angle only exists when light starts in the higher-index medium, so first compare with .

2. Use the critical-angle relation

When , use .

3. Evaluate the threshold

Critical-angle result

The current incident angle is 4.86^\circ above the critical angle, so the refracted branch has already ended.

Common misconception

Any large incident angle can give total internal reflection if the boundary is steep enough.

A large angle by itself is not enough. The light must be going from higher n to lower n so that a real critical angle exists in the first place.

If n_1 is not larger than n_2, Snell's law still gives a real transmitted angle no matter how far you raise theta_1 within this model's range.

Mini challenge

Keep the incident angle fixed above the glass-to-air critical angle, then raise n_2 closer to n_1. Before you test it, what should happen to the threshold?

Make a prediction before you reveal the next step.

Decide whether theta_c rises or falls, and whether the same ray is more or less likely to keep reflecting internally.

Check your reasoning against the live bench.

The critical angle rises, so the same incident angle becomes less likely to stay in total internal reflection.
Raising n_2 closer to n_1 reduces the index contrast, so n_2 / n_1 gets larger and theta_c increases. A setup that used to be above the threshold can drop back into ordinary refraction.

Quick test

Reasoning

Question 1 of 4

Reason from the threshold, not from a slogan. Use the index contrast, the critical angle, and the branch that still exists on the live boundary.

Which condition must be true before total internal reflection can happen at all?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows a horizontal boundary between a top medium and a bottom medium, with a dashed normal line through the contact point. One incoming ray approaches from the upper left. Below the critical angle a transmitted ray leaves into the lower right, and above the critical angle the outgoing branch stays in the top medium as a reflected ray.

Optional overlays show the normal and angle markers, the critical-angle threshold, the equal-angle reflection cue used after the threshold, and the speed labels tied to the current refractive indices.

Graph summary

The threshold transition graph plots angle from the normal against incident angle for the current media pair. The transmitted branch rises toward 90 degrees at the critical angle, and beyond that point the reflected branch continues because the ray remains in the first medium.

The transmitted-angle graph isolates the ordinary-refraction branch below threshold, so hovering it previews another boundary setup rather than a later time.